Nonparametric Finance

Chapter 6Prediction

We concentrate on prediction with nonparametric smoothing. Nonparametric smoothing can be divided into time and state space smoothing. Time space smoothing means that we use moving averages and state space smoothing means that we use kernel regression with state variables (external explanatory variables). The prediction formulas of ARMA and GARCH processes are related to time and state space smoothing. These prediction formulas are given in Section 5.3, where time series models are considered. Section 5.2 considers the combination of time and state space smoothing with parametric models.

Our emphasis will be more on the economic significance than on the statistical significance. We say that a prediction method is economically significant if it can produce portfolios with significantly higher Sharpe ratios than the Sharpe ratios of the portfolios that are constructed without prediction methods. However, looking at the sum of squared prediction errors can give insights into the underlying reasons for the economic significance.

The classical theory of efficient markets says that the asset returns are unpredictable. If the asset returns were predictable, investors would buy the assets whose predicted returns are high, and eventually this buying would increase the prices and distort the predicted returns. However, it is possible that risk aversion of investors makes the asset returns predictable. For example, in a recession the expected returns could be high but ...